Abstract
We consider matrix integrable fifth-order mKdV equations via a kind of group reductions of the Ablowitz-Kaup-Newell-Segur matrix spectral problems. Based on properties of eigenvalue and adjoint eigenvalue problems, we solve the corresponding Riemann-Hilbert problems, where eigenvalues could equal adjoint eigenvalues, and construct their soliton solutions, when there are zero reflection coefficients. Illustrative examples of scalar and two-component integrable fifth-order mKdV equations are given.